Quadratic spin-phonon coupling and bipolarons in trapped ions

TL;DR

This paper proposes a method for quantum simulation of quadratic spin-phonon interactions in trapped ions, demonstrating the emergence and pinning of bipolarons influenced by temperature, with potential for studying complex quantum phenomena.

Contribution

It introduces a novel scheme to simulate quadratic spin-phonon coupling in trapped ions using optical tweezers and Mølmer-Sørensen interactions, enabling exploration of bipolaron dynamics.

Findings

Bipolarons emerge due to zero-point energy of phonons.

Thermal occupation can pin bipolarons at finite temperature.

The scheme allows studying bipolaron mobility as a function of temperature.

Abstract

We consider the quantum simulation of quadratic spin-phonon coupling in a crystal of trapped ions. The coupling is implemented using tightly focused optical tweezers on each ion that change the local trapping potential in a state-dependent way. By encoding spins in the internal states of the ions and adding a tunneling term via M{\o}lmer-S{\o}rensen-type interactions, we calculate the emergence of mobile bipolarons driven by the zero-point energy of the ion crystal phonons. We show that thermal occupation may pin the bipolarons for ion crystals at finite temperature. Our scheme can be used to study and illustrate the emergence of mobile bipolarons as a function of temperature.